cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A066364 Prime divisors of solutions to 10^n == 1 (mod n).

Original entry on oeis.org

3, 37, 163, 757, 1999, 5477, 8803, 9397, 13627, 15649, 36187, 40879, 62597, 106277, 147853, 161839, 215893, 231643, 281683, 295759, 313471, 333667, 338293, 478243, 490573, 607837, 647357, 743933, 988643, 1014877, 1056241, 1168711, 1353173, 1390757, 1487867, 1519591, 1627523, 1835083, 1912969, 2028119, 2029759, 2064529
Offset: 1

Views

Author

Vladeta Jovovic, Dec 21 2001

Keywords

Examples

			10^27-1 = 3^5*37*757*333667*440334654777631 is a solution to the congruence.

Links

Crossrefs

Cf. A014950, A001270, A027889, A007138, A114207.

Programs

  • Mathematica
    fQ[p_] := Block[{fi = First@# & /@ FactorInteger[ MultiplicativeOrder[ 10, p]]}, Union[ MemberQ[ lst, #] & /@ fi] == {True}]; k = 4; lst = {3}; While[k < 180000, If[ p = Prime@ k; fQ@ p, AppendTo[ lst, p]; Print@ p]; k++]; lst (* Robert G. Wilson v, Nov 30 2013 *)
  • PARI
    S=Set([3]); forprime(p=7,10^6, v=factorint(znorder(Mod(10,p)))[,1]; if(length(setintersect(S,Set(v)))==length(v), S=setunion(S,[p])) ); print(vecsort(eval(S))) \\ Max Alekseyev, Nov 16 2005

Formula

A prime p is a term iff all prime divisors of ord_p(10) are terms, where ord_p(10) is the order of 10 modulo p. - Max Alekseyev, Nov 16 2005

Extensions

Edited by Max Alekseyev, Nov 16 2005
Edited by Hans Havermann, Jul 11 2014

A102146 a(n) = sigma(10^n - 1), where sigma(n) is the sum of positive divisors of n.

Original entry on oeis.org

13, 156, 1520, 15912, 148512, 2042880, 14508000, 162493344, 1534205464, 16203253248, 144451398000, 2063316971520, 14903272088640, 158269280832000, 1614847741624320, 17205180696931968, 144444514193267496
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 14 2005

Keywords

Links

Crossrefs

Cf. A000203, A001270, A002283, A003020, A005422, A046053, A046107, A046412, A046415, A046416, A046417, A046418, A046419, A046420, A057951, A059892, A061075, A070528, A070529, A081317, A081318, A085035, A095370, A095413, A095414, A095417, A095418, A102347, A102380, A112505, A147556, A295503, A366669.

Programs

  • Mathematica
    DivisorSigma[1,10^Range[20]-1] (* Harvey P. Dale, Jan 05 2012 *)
  • PARI
    a(n) = sigma(10^n-1); \\ Michel Marcus, Apr 22 2017

Formula

a(n) = A000203(A002283(n)). - Ray Chandler, Apr 22 2017

A106305 Divisors of 10^14 - 1.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 239, 717, 2151, 2629, 4649, 7887, 13947, 23661, 41841, 51139, 153417, 460251, 909091, 1111111, 2727273, 3333333, 8181819, 9999999, 10000001, 12222221, 30000003, 36666663, 90000009, 109999989, 217272749, 651818247
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 12 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A001270, A007138, A046107, A112505.

Programs

Formula

10^14 - 1 = 3^2 * 11 * 239 * 4649 * 909091 = 99999999999999. - Alonso del Arte, Nov 09 2017

A109933 Divisors of 10^13 - 1.

Original entry on oeis.org

1, 3, 9, 53, 79, 159, 237, 477, 711, 4187, 12561, 37683, 265371653, 796114959, 2388344877, 14064697609, 20964360587, 42194092827, 62893081761, 126582278481, 188679245283, 1111111111111, 3333333333333, 9999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 11 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A001270, A007138, A046107.

Programs

A111117 Divisors of 10^15 - 1.

Original entry on oeis.org

1, 3, 9, 27, 31, 37, 41, 93, 111, 123, 271, 279, 333, 369, 813, 837, 999, 1107, 1147, 1271, 1517, 2439, 3441, 3813, 4551, 7317, 8401, 10027, 10323, 11111, 11439, 13653, 25203, 30081, 30969, 33333, 34317, 40959, 47027, 75609, 90243, 99999, 141081
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 15 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A001270, A007138, A046107, A112505.

Programs

A111211 Divisors of 10^16 - 1.

Original entry on oeis.org

1, 3, 9, 11, 17, 33, 51, 73, 99, 101, 137, 153, 187, 219, 303, 411, 561, 657, 803, 909, 1111, 1233, 1241, 1507, 1683, 1717, 2329, 2409, 3333, 3723, 4521, 5151, 6987, 7227, 7373, 9999, 10001, 11169, 13563, 13651, 13837, 15453, 18887, 20961, 22119, 25619
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 25 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A001270, A007138, A046107, A112505.

Programs

A113522 Divisors of 10^18 - 1.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 19, 21, 27, 33, 37, 39, 57, 63, 77, 81, 91, 99, 111, 117, 133, 143, 171, 189, 209, 231, 247, 259, 273, 297, 333, 351, 399, 407, 429, 481, 513, 567, 627, 693, 703, 741, 777, 819, 891, 999, 1001, 1053, 1197, 1221, 1287, 1443, 1463, 1539, 1729
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 12 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A001270, A007138, A046107, A112505.

Programs

A113116 Divisors of 10^17 - 1.

Original entry on oeis.org

1, 3, 9, 2071723, 6215169, 18645507, 5363222357, 16089667071, 48269001213, 11111111111111111, 33333333333333333, 99999999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 02 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A001270, A007138, A046107, A112505.

Programs

Showing 1-8 of 8 results.

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